The generator matrix

1 0 0 0 0 0 0 1 1 1 2 0 0 2 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 2 2 1 0 2 0 2 1 1 1 1 1 0 0 2 1 0 0 1 2 1 1 1 1 0 1 2 1 1 2 1 0 1 1 2 1 0 1
0 1 0 0 0 0 0 0 0 0 0 1 2 1 1 1 1 1 1 1 1 3 0 1 2 2 0 0 1 2 1 3 1 0 1 0 0 3 2 3 2 1 0 0 1 2 1 3 1 3 2 0 0 1 2 1 3 1 1 0 2 3 3 0 0 1 0
0 0 1 0 0 0 0 0 0 0 0 0 1 3 1 3 1 1 1 3 0 2 1 2 1 3 1 1 2 1 3 0 1 0 2 1 2 0 0 1 3 1 2 1 1 2 0 0 1 1 0 0 3 3 1 0 2 3 0 3 2 2 1 1 3 3 1
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 2 2 0 2 2 2 0 0 0 2 2 0 2 0 2 0 2 1 1 1 3 3 1 1 1 1 1 3 3 3 3 1 3 1 3 3 0 3 1 2 1 1 3 2 1 3 0 1
0 0 0 0 1 0 0 0 1 1 1 2 0 1 0 3 2 0 3 1 3 2 0 3 0 1 2 1 2 1 0 1 0 1 0 2 2 1 3 0 1 1 0 1 3 1 1 2 0 1 2 3 2 3 2 3 0 0 0 1 1 1 3 3 1 2 3
0 0 0 0 0 1 0 1 0 1 3 2 0 3 0 1 1 3 2 2 3 0 0 3 1 2 1 3 3 0 0 2 1 2 3 3 2 2 2 2 0 3 1 2 2 0 2 3 0 1 1 0 3 3 2 3 2 0 3 2 3 1 1 0 1 2 3
0 0 0 0 0 0 1 1 3 2 1 1 1 2 3 3 0 3 2 3 0 2 1 1 0 2 3 1 1 3 2 3 1 0 0 1 2 1 1 1 2 0 2 3 2 2 0 1 2 3 2 1 0 2 2 3 0 0 0 1 2 0 0 0 1 2 0
0 0 0 0 0 0 0 2 2 0 2 2 2 0 2 2 0 2 0 2 0 0 2 2 0 0 2 0 0 0 2 0 0 2 2 0 2 2 0 2 2 2 0 2 2 2 2 2 0 0 0 0 0 0 2 0 2 0 2 0 0 2 2 0 2 2 2

generates a code of length 67 over Z4 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+98x^53+153x^54+310x^55+532x^56+650x^57+839x^58+980x^59+1189x^60+1348x^61+1388x^62+1720x^63+1974x^64+1918x^65+1961x^66+2128x^67+2225x^68+2084x^69+2018x^70+1874x^71+1600x^72+1418x^73+1118x^74+896x^75+751x^76+536x^77+396x^78+256x^79+154x^80+126x^81+57x^82+28x^83+19x^84+14x^85+5x^86+2x^88+1x^90+1x^112

The gray image is a code over GF(2) with n=134, k=15 and d=53.
This code was found by Heurico 1.10 in 63 seconds.